International Journal of Science, Technology and Society 2021; 9(6): 263-274 http://www.sciencepublishinggroup.com/j/ijsts doi: 10.11648/j.ijsts.20210906.12 ISSN: 2330-7412 (Print); ISSN: 2330-7420 (Online) Computation Programming of McCabe-Thiele and Ponchon-Savarit Methods for SHORT-CUT Distillation Design Chavdar Chilev 1, 2, * , Moussa Dicko 2 , Patrick Langlois 2 , Farida Lamari 2 1 Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria 2 Chemical Engineering, CNRS LSPM University Sorbonne Paris Nord, Villetaneuse, France Email address: * Corresponding author To cite this article: Chavdar Chilev, Moussa Dicko, Patrick Langlois, Farida Lamari. Computation Programming of McCabe-Thiele and Ponchon-Savarit Methods for SHORT-CUT Distillation Design. International Journal of Science, Technology and Society. Vol. 9, No. 6, 2021, pp. 263-274. doi: 10.11648/j.ijsts.20210906.12 Received: October 3, 2021; Accepted: October 25, 2021; Published: November 5, 2021 Abstract: Using modern computer programming resources, a computer code has been developed in the MatLAB programming environment, which allows the use of the McCabe-Thiele and Ponchon-Savarit methods for SHORT-CUT distillation design. The McCabe-Thiele and Ponchon-Savarit methods are easy to apply, are not time consuming, and allow the easy visualization of the interrelationships among variables. In order to describe all the programming steps of these methods, a combination of different types of MatLAB functions has been used. The optimum reflux ratio is determined by using volume criteria, whichallows minimizing the volume of the distillation column and thereby reducing the total cost of a distillation unit. To evaluate the accuracy of the results, a comparison between the results produced by graphical methods and those calculated by other SHORT-CUT methods and rigorous calculations has been carried out. To perform this, the ChemCAD 7.1.5 simulator has been used. The SHORT-CUT distillation module in this simulator uses the Fenske-Underwood-Gilliland (FUG) method. For rigorous estimation, the SCDS multi-stage vapor-liquid equilibrium module in ChemCAD software environment has been used. SCDS is a rigorous multi-stage vapor-liquid equilibrium module which simulates any single column calculation including distillation columns, absorbers, reboiler and strippers. The results produced by graphical methods are closer to the rigorous-calculation results than to the FUG SHORT-CUT method ones, with respect both to the reflux ratio and to the bottom and top light-key mass fraction. Keywords: Distillation, Short-Cut Methods, Computer Simulations, McCabe-Thiele, Ponchon-Savarit 1. Introduction Before the advent of the modern digital computer, various "SHORT-CUT" methods had been developed to simplify the task of designing multicomponent distillation columns. Though computer programs would normally be available for the rigorous-solution equations, SHORT-CUT methods are still useful in the preliminary design work, and as an aid in defining problems for computer solution. Intelligent use of the SHORT-CUT methods can indeed reduce both computer time and costs. The SHORT-CUT methods available for distillation design processes can be divided into two classes: empirical methods and simplified methods [1-3]. The first ones are based on the performance of operating columns and on results of rigorous designs. Typical examples of these methods are the Gilliland's [4] and the Erbar-Maddox correlations [5]. The other methods are based on the simplification of the rigorous stage-by-stage procedures in order to enable the calculations to be done by using hand calculators or graphically. Typical examples of this approach are the McCabe-Thiele [6] and the Ponchon-Savarit methods [7, 8]. The first class of methods has been implanted in modern simulation software such as ASPEN ONE, ChemCAD, or ProSIM while the McCabe-Thiele and Ponchon-Savarit methods are two graphical methods used for the design of
12
Embed
Computation Programming of McCabe-Thiele and Ponchon ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
International Journal of Science, Technology and Society 2021; 9(6): 263-274
http://www.sciencepublishinggroup.com/j/ijsts
doi: 10.11648/j.ijsts.20210906.12
ISSN: 2330-7412 (Print); ISSN: 2330-7420 (Online)
Computation Programming of McCabe-Thiele and Ponchon-Savarit Methods for SHORT-CUT Distillation Design
Chavdar Chilev1, 2, *
, Moussa Dicko2, Patrick Langlois
2, Farida Lamari
2
1Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria 2Chemical Engineering, CNRS LSPM University Sorbonne Paris Nord, Villetaneuse, France
Email address:
*Corresponding author
To cite this article: Chavdar Chilev, Moussa Dicko, Patrick Langlois, Farida Lamari. Computation Programming of McCabe-Thiele and Ponchon-Savarit
Methods for SHORT-CUT Distillation Design. International Journal of Science, Technology and Society. Vol. 9, No. 6, 2021, pp. 263-274.
doi: 10.11648/j.ijsts.20210906.12
Received: October 3, 2021; Accepted: October 25, 2021; Published: November 5, 2021
Abstract: Using modern computer programming resources, a computer code has been developed in the MatLAB
programming environment, which allows the use of the McCabe-Thiele and Ponchon-Savarit methods for SHORT-CUT
distillation design. The McCabe-Thiele and Ponchon-Savarit methods are easy to apply, are not time consuming, and allow the
easy visualization of the interrelationships among variables. In order to describe all the programming steps of these methods, a
combination of different types of MatLAB functions has been used. The optimum reflux ratio is determined by using volume
criteria, whichallows minimizing the volume of the distillation column and thereby reducing the total cost of a distillation unit.
To evaluate the accuracy of the results, a comparison between the results produced by graphical methods and those calculated
by other SHORT-CUT methods and rigorous calculations has been carried out. To perform this, the ChemCAD 7.1.5 simulator
has been used. The SHORT-CUT distillation module in this simulator uses the Fenske-Underwood-Gilliland (FUG) method.
For rigorous estimation, the SCDS multi-stage vapor-liquid equilibrium module in ChemCAD software environment has been
used. SCDS is a rigorous multi-stage vapor-liquid equilibrium module which simulates any single column calculation
including distillation columns, absorbers, reboiler and strippers. The results produced by graphical methods are closer to the
rigorous-calculation results than to the FUG SHORT-CUT method ones, with respect both to the reflux ratio and to the bottom
Number of theoretical stages for rectifying section 1.93033 1.87722
Number of theoretical stages for stripping section 2.05526 2.2299
Total number of theoretical stages 3.98559 4.10713
Top �� mass fraction 0.95 0.95
Bottom�� mass fraction 0.03 0.03
Table 2. Results for the acetone/n-butanol system.
Parameter FUG with Fenske feed stage location FUG with Kirkbride feed stage location
Minimum reflux ratio 2.77 × 10(� 2.77 × 10(�
Optimum reflux ratio 7.77 × 10(� 7.77 × 10(�
Total number of theoretical stages 6.43 6.43
Feed stage location 3.92 4.24
Top �� mass fraction 9.76 × 10(� 9.76 × 10(�
Bottom�� mass fraction 6.16 × 10(P 6.16 × 10(P
In order to verify the possibility of using both graphical
methods for SHORT-CUT distillation design, the acetone/n-
butanol system has been modeled by conventional SHORT-
CUT methods. To perform this simulation, the ChemCAD
7.1.5 simulator has been used. The shortcut distillation module
in the simulator uses the Fenske-Underwood-Gilliland (FUG)
method [4, 24, 25] to simulate a simple distillation column.
The feed location can be calculated by the Fenske [24] or
Kirkbride [26] equations. In order to determine the
thermodynamic of the system, the same experimental data for
the vapor/liquid equilibrium [15] and NRTL model have been
used [27, 28]. The use of ChemCAD allowed regress
experimental data and generate binary interaction parameters
(BIP) for mixtures. The results of the simulation for the
acetone/n-butanol system are shown in Table 2.
The only difference between the two methods in the
International Journal of Science, Technology and Society 2021; 9(6): 263-274 272
ChemCAD shortcut distillation module is about the feed
stage location. The results are however very close for this
parameter and basically show the same feed stage
locationc� ≈ 4.
In the FUG method, the reflux ratio ) or the ratio ) )-./⁄
must be specified. Thus, there is no possibility to obtain the
optimum reflux ratio. If ) )-./⁄ is set, ChemCAD first
calculates )-./ and then determines )*+, as ) )-./⁄ ratio.
Determination of )-./ in the ChemCAD shortcut distillation
module is performed by the Underwood procedure [25].
The resulting value is )-./ � 0.277358 whereas )-./ �0.285235 is obtained if using graphical methods. The two
values are very close, which is a criterion showing the ability
to use graphical methods for SHORT-CUT distillation design.
In the ChemCAD shortcut distillation module, a case study
option is provided to allow to vary ) )-./⁄ in a specified
range and review its effect on column performance indicators
such as the number of stages or the final product concentration.
Figure 6. Sensitive study for influence of ) )-./⁄ on the final �� concentration.
On Figure 6, the sensitive analyses to check the influence
of ) )-./⁄ on the final �� mass fraction in the distillate and
in the bottom product are shown. The figure shows that the
change in ) )-./⁄ does not affect the final �� mass fraction.
The desired value of �� mass fraction in the distillate is
�� � 0.95 whereas the value of this parameter obtained by
ChemCAD shortcut module is �� � 0.98. The desired value
of �� mass fraction in the bottom product is �� � 0.030
whereas the value of that parameter obtained by ChemCAD
shortcut module is �� � 0.062. Thus, according to the FUG
SHORT-CUT method, the separation of the acetone/n-
butanol system by rectification makes it impossible to obtain
the bottom product with �� mass fraction �� � 0.03.
Figure 7. Sensitive study for influence of ) )-./⁄ on the total number of stages.
On Figure 7 the sensitive analyses to check the influence
of ) )-./⁄ on the total number of stages is shown. It can be
seen from the figure that after ) )-./⁄ w 2.8, the reduction
of the total number of stages is very slight. Thus, ) )-./⁄ �2.8 is the optimum ratio and the value )*+, � 0.78 for the
optimum reflux ratio is then obtained. Determining )*+, in
273 Chavdar Chilev et al.: Computation Programming of McCabe-Thiele and Ponchon-Savarit Methods for
SHORT-CUT Distillation Design
this way is however not very accurate because it takes into
account the influence of ) only on the total number of stages
but not on the total cost of a distillation unit. Therefore,
defining )*+, using the MatLAB code, as proposed here, has
an advantage over the FUG method for the following two
main reasons:
1. The sensitive-analysis option is additional and not
integrated into the FUG SHORT-CUT method itself.
Thus, after determining the number of stages, further
research must be conducted to determine )*+,, whereas
the MatLAB code suggested here directly determines
)*+, based on the volume criteria (see part 2.4);
2. Determination of )*+, by sensitive analyses in the FUG
SHORT-CUT method does not take into account the
total cost of a distillation unit whereas the volume
criteria in the MatLAB code (see function F = N (R + 1)
in part 2.4) account for the total cost of a distillation
unit. Therefore, defining )*+, is much more accurate.
For comparison to the SHORT-CUT methods proposed
here (graphical and FUG methods), a rigorous calculation has
been made by using the SCDS module in the ChemCAD
simulator.
SCDS is a rigorous multi-stage vapor-liquid equilibrium
module which simulates any single column calculation [13].
This module is mainly designed to simulate non-ideal
� − ���x chemical systems. It uses a Newton-Raphson
convergence method and calculates the derivatives of each
equation rigorously.
The calculation algorithm of the SCDS module requires to
initially setting the number of theoretical stages and the feed
stage location. Then as a result of the solution the
concentration of LK in the top and the bottom of the column
is obtained. In this case, in order to make a comparison
between the rigorous and SHORT-CUT methods, the number
of theoretical stages 5 and the feed stage location 3 are
selected. SCDS offers a variety of specifications, such as
total mole flow rate, heat duty, reflux ratio, boil-up ratio,
temperature etc. Therefore, there are several different ways to
initially define the SDST module. The results obtained by
SCDS modulates for the acetone/n-butanol system are
presented in Table 3.
Table 3. Rigorous results obtained for the acetone/n-butanol system via the
SCDS module.
Parameter SCDS module
Reflux ratio 0.7
Total number of theoretical stages 5
Feed stage location 3
Top �� mass fraction 0.95149058
Bottom�� mass fraction 0.03
The results in Table 3 show that there is little difference
between the SHORT-CUT and the rigorous calculation. For
comparison in terms of accuracy between the graphical
methods and the FUG method in ChemCAD shortcut
distillation module, the differences are indicated: on the one
hand between the FUG method and the rigorous calculation,
on the other hand between graphical methods and the
rigorous calculation.
1. The rigorous calculations show that the desired end
results are achieved by the reflux ratio ) = 0.7. This
value is closer to the optimum reflux ratio obtained by
the Ponchon-Savarit method rather than by the FUG
method;
2. The rigorous calculation gives a total number of 5
theoretical stages. For this parameter, the graphical
methods give 4 while the FUG method gives 6. The
difference between the rigorous calculation and all
SHORT-CUT methods is thus the same;
3. The rigorous calculations show that it is possible to
obtain distillate with the �� mass fraction �� =0.95149058, and the bottom product with the LK mass
fraction �� = 0.03 . According to the results of the
graphical methods (see Table 1), this is possible whereas
the sensitive analyses of the FUG method (see Figure 6)
show that this is not possible. According to Figure 6, the
minimum bottom �� mass fraction is �� =0.06156551. Thus, with respect to the bottom and top
�� mass fraction, the results of graphical methods
practically coincide with the rigorous calculation.
4. Conclusion
A MatLab code for SHORT-CUT distillation design using
the McCabe-Thiele and Ponchon-Savarit methods is
proposed, in the first place because those methods are easy to
apply and are not time consuming, and moreover because
they allow for the easy visualization of the interrelationships
among variables. By the combination of the two functions
����� and ����� , experimental vapor-liquid equilibrium
data and enthalpy data for both phases have been
approximated. In the studied system, this approximation has
given very accurate results. In order to obtain a basic
estimation of both methods, a combination of several
MatLAB functions such as "�O����O��", "�O����T", "M��", and "M��"has been used.
The volume criterion has been defined and used to
determine the optimum reflux ratio )*+, , which allows
minimizing the volume of the column and thereby reducing
the total cost of a distillation unit. The sensitive analyses for
number of working reflux ratios ). in the range of 1,1)-./ to
10)-./10 have been made. The number of ). was varied
from 10 to 1000. It was found that for ). > 200, no changes
in the determination of )*+, occurred. Thus, in this study,
). = 200 has been used. Notwithstanding this result, the
MatLAB code provides an opportunity to set the number of
working reflux ratios )..
To evaluate the accuracy of the results obtained with the
graphical methods via the generated MatLab code, a
comparison with the results calculated by other SHORT-CUT
methods and rigorous calculations has been performed. The
ChemCAD 7.1.5 simulator has been used for this
comparison; its shortcut distillation module uses the Fenske-
Underwood-Gilliland (FUG) method. For rigorous
estimation, the SCDS multi-stage vapor-liquid equilibrium
International Journal of Science, Technology and Society 2021; 9(6): 263-274 274
module has been used.
The results show that the graphical methods are closer to
the results of rigorous calculations than the FUG SHORT-
CUT method. This is both with respect to the reflux ratio and
to the bottom and top �� mass fraction. It can therefore be
concluded that the McCabe-Thiele and Ponchon-Savarit
graphical methods can be successfully used for SHORT-CUT
distillation design. The main advantage of these methods
over the FUG method in the ChemCAD shortcut distillation
module is the criterion defined in Part 2.4 to determine the
optimal reflux ratio.
Acknowledgements
The authors are grateful to « Invited Fellow protocol » of
University Sorbonne Paris Nord which has contributed to
enhance the collaboration of joint innovative research
between UCTM Sofia and LSPM CNRS UPR3407.
References
[1] Kong L, Maravelias CT (2020). Generalized short-cut distillation column modeling for superstructure-based process synthesis. AIChE J., 66 (2). https://doi.org/10.1002/aic.16809
[2] Adiche Ch., Vogelpohl A. (2011). Short-cut methods for the optimal design of simple and complex distillation columns. ChERD, 89 (8), 1321-1332.
[3] Zubira M. A. et al. (2019). Economic, Feasibility, and Sustainability Analysis of Energy Efficient Distillation Based Separation Processes. Chem. Eng. Transactions, 72, 109-114.
[4] Gilliland E. R. (1940). Multicomponent Rectification Estimation of the Number of Theoretical Plates as a Function of the Reflux Ratio. Ind. Eng. Chem., 32 (9), 1220-1223.
[5] Erbar J. H., Maddox R. N. (1961). Latest score: reflux vs. Trays. Pet. Ref., 40 (5), 183.
[6] McCabe W. L, Thiele W. E (1925). Graphical Design of Fractionating Columns. Ind. Eng. Chem., 17 (6), 605-611.
[7] Ponchon M. (1921). Graphical study of distillation. Tech. Modern, 13, 20.
[8] Savarit R. (1922). Definition of Distillation, Simple Discontinuous Distillation, Theory and Operation of Distillation Column, and Exhausting and Concentrating Columns for Liquid and Gaseous Mixtures and Graphical Methods for Their Determination. Arts et Metiers, 3, 65.
[9] Mohapatro R. N. et al. (2021). Separation Efficiency Optimisation of Toluene–Benzene Fraction using Binary Distillation Column. J. Inst. Eng. India Ser., D 102, 125–129.
[10] Seedat N., Kauchali Sh., Patel B. (2021). A graphical method for the preliminary design of ternary simple distillation columns at finite reflux. South African Journal of Chemical Engineering, 37, 99-109.
[11] Taifan G. S. P., Maravelias Ch. T. (2020). Integration of graphical approaches into optimization-based design of multistage liquid extraction. Computers & Chemical Engineering, 143 (5), 107126.
[12] Yeoh K. P., Hui Ch. W. (2021). Rigorous NLP distillation models for simultaneous optimization to reduce utility and capital costs. Cleaner Engineering and Technology, 2, 100066.
[13] Kister, R. (1990). Distillation Design, McGraw-Hill.
[14] Wehe A. H., Coates J. (1955). Vapor-liquid equilibrium relations predicted by thermodynamic examinations of activity coefficients. AIChE J., 1 (2), 241-246.
[15] Michalski H., Michalowski S., Serwinski M., Strumillo C. (1961). Vapour - Liquid Equilibria for the System Acetone - n-Butanol. Zesz. Nauk. Politech. Lodz. Chem., 10 (36), 73-84.
[16] Milton R., Chandler E., Brown S. F. (2021). Analysing the robustness of multi-stage bioseparations to measurement errors. Computer Aided Chemical Engineering, 50, 393-398.
[17] Haan A. B., Eral H. B., Schuur B. (2020), Chapter 2. Evaporation and Distillation. Industrial Separation Processes: Fundamentals, Berlin, Boston: De Gruyter, 17-56.
[18] Morgan D. L. (2007), Use of transformed correlations to help screen and populate properties within databanks, Fluid Phase Equilib., 256, 54-61.
[19] Ghosh S., Seethamraju S. (2020). Reactive Distillation for Methanol Synthesis: Parametric Studies and Optimization Using a Non-polar Solvent. Process Integr Optim Sustain, 4, 325–342.
[20] Mahsa K., Abdoli S. M., (2021). The Design and Optimization of Extractive Distillation for Separating the Acetone/n-Heptane Binary Azeotrope Mixture. ACS Omega, 6 (34), 22447–22453.
[21] Wankat, P. C. (2007). Separation Process Engineering, 2nd Ed., Prentice Hall.
[22] Frank O. (1977). Shortcuts for Distillation Design. Chem. Ing. March, 14, 110-124.
[23] Van Winkle M., Todd W. G. (1971), Optimum Fractionation Design by Simple Graphical Methods, Chem. Eng., 136.
[24] Fenske M. R. (1932). Fractionation of Straight-Run Pennsylvania Gasoline. Ind. Eng. Chem., 24 (5), 482-485.
[25] Underwood A. J. V. (1948). Fractional Distillation of Multicomponent Mixtures. Chem. Eng. Proc., 44 (8), 603-614.
[26] Kirkbridge C. G. (1944). Process Design Procedure for. Multicomponent Fractionators. Pet. Ref., 23 (9), 321-336.
[27] Renon H., Prausnitz J. M. (1968). Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, AIChE J., 14 (1), 135-144.
[28] Maurer G., Prausnitz J. M. (1978). Fluid Phase Equilibria, 2 (2), 91-99.